This is the second part of the reproducible analysis supporting the findings of the manuscript entitled “Response diversity in the context of multifarious environmental change”. Here, we are going to produce the data necessary to reproduce the figures presented in the manuscript, and to analyse the relative results.
We hypothesised that multiple factors may shape response diversity in a multifarious environmental change context. Specifically, we are going to investigate whether the three following factors may drive response diversity: I. The relative strength of effect of different environmental drivers. II. Correlation in species’ responses to different environmental drivers. III. Mean value of environmental conditions.
Initially, we also hypothesised that the different correlation scenarios of temperature and salinity change over time may be driving response diversity. However, after thinking and discussing the hypothesis, we concluded that there was no reason to believe that. Yet, we used different correlation scenarios in salinity and temperature change in the simulation to show that our results are robust to every kind of environmental change scenario.
In this document, we first analyse the II and III determinants, and then we repeat the analysis in a case where temperature and salinity have exactly the same effect on species growth rate (determinant I).
For each community, we calculate first response capacity (with unknown direction of environmental change), and then also response diversity for each environmental change scenario. We here quantify directional response diversity also as dissimilarity. However, we decided to exclude this measurement of response diversity, as it does not correlate well with community stability, and it also shows to be dependent on the shape of species responses. In the manuscript, thus, we focus on divergence as main metric to measure directional response diversity.
Within the project “response diversity in the context of multifarious environmental change”, we have been simulating species response curves using the Eppley performance curve.
With one environmental variable, the performance (i.e., rate) is given by:
Adding a second environmental variable gives:
\(rate(E_1, E_2) = a_1e^{b_1E_1}(1 - (\frac{E_1 - z_1}{w_1/2})^2) + a_2e^{b_2E_2}(1 - (\frac{E_2 - z_2}{w_2/2})^2)\)
We now want to assess the role of diversity in response to one (or both) environmental variable(s) influence response diversity.
To do that, we are going to manipulate amount of diversity in responses to one or both env variables among the species, and also the correlation in the tolerances (position of optima, determine by the terms z1 and z2 in the above formula). We will make scenarios of communities with diversity in response to only E1 (temperature), or both E1 (temperature) and E2 (salinity), with diversity in both that is positively correlated or negatively.
# Variation in diversity in z1
We now create 3 communities. Community 1 is characterized by low diversity in z1, community 2 has medium diversity in z1, and community 3 has high diversity in z1. z2 is constant in the 3 communities and fixed to a medium level of diversity.
E1 and E2 have negative correlation. We create 3 scenarios where we keep the variation of E1 and E2 fixed, but we change the mean so that in the first scenario E1 and E2 have low mean value, in the second medium, and high in the third (factor III).
(#fig:plotcomm1_neg)Community 1, single species responses. (a) Species responses to the gradient of temperature. Different colour lines show the dependency of the rate to the second environmental variable (salinity). (b) Species responses to the gradient of salinity. Different colour lines show the dependency of the rate to the second environmental variable (temperature).
(#fig:plotcomm2_neg)Community 2, single species responses. (a) Species responses to the gradient of temperature. Different colour lines show the dependency of the rate to the second environmental variable (salinity). (b) Species responses to the gradient of salinity. Different colour lines show the dependency of the rate to the second environmental variable (temperature).
(#fig:plotcomm3_neg) Community 3, single species responses. (a) Species responses to the gradient of temperature. Different colour lines show the dependency of the rate to the second environmental variable (salinity). (b) Species responses to the gradient of salinity. Different colour lines show the dependency of the rate to the second environmental variable (temperature).
Here and elsewhere in this document, the position of the optima has been estimated as the environmental location (E1 and E2 values) for which the rate is maximum.
Increasing variance in z1 - positive correlation between env variables (E1 and E2)
Same steps as before (3 communities with increasing diversity in z1 while z2 is fixed), but the correlation between E1 and E1 is positive
Increasing variance in z1 - no correlation between env variables (E1 and E2)
Same steps as before (3 communities with increasing diversity in z1 while z2 is fixed), but there is no correlation between E1 and E1
Now we do the same, but having also z2 changing together with z1 with positive correlation. So, diversity in z1 and z2 are increasing gradually from low to high in the 3 communities.
Increasing variance in z1 and z2 - negative correlation between environmental variables (E1 and E2).
We now create 3 communities. Community 1 is characterized by low diversity in z1 and z2, community 2 has medium diversity in z1 and z2, and community 3 has high diversity in z1 and z2.
E1 and E2 fluctuate with negative correlation.
(#fig:plotcomm1_pos)Community 1, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
(#fig:plotcomm2_pos)Community 2, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
(#fig:plotcomm3_pos) Community 3, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
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Increasing variance in z1 and z2 - positive correlation between env variables (E1 and E2)
Same steps as before (3 communities with increasing diversity in z1 while z2 is fixed), but the correlation between E1 and E1 is positive
Increasing variance in z1 - no correlation between env variables (E1 and E2)
Same steps as before (3 communities with increasing diversity in z1 while z2 is fixed), but there is no correlation between E1 and E1
Now we do the same, but having also z2 changing together with z1 with negative correlation. So, diversity in z1 is increasing gradually from low to high in the 3 communities, while z2 decreases gradually in the 3 communities.
Increasing variance in z1 and z2 - negative correlation between env variables (E1 and E2).
We now create 3 communities. Community 1 is characterized by low diversity in z1 and high diversity in z2, community 2 has medium diversity in z1 and z2, and community 3 has high diversity in z1 and low in z2.
E1 and E2 have negative correlation.
(#fig:plotcomm1_mix)Community 1, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
(#fig:plotcomm2_mix)Community 2, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
(#fig:plotcomm3_mix) Community 3, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
Here and elsewhere in this document, the position of the optima has been estimated as the environmental location (E1 and E2 values) for which the rate is maximum.
Increasing variance in z1 and z2 - positive correlation between env variables (E1 and E2)
Same steps as before (3 communities with increasing diversity in z1 while z2 is fixed), but the correlation between E1 and E1 is positive
Increasing variance in z1 - no correlation between env variables (E1 and E2)
Same steps as before (3 communities with increasing diversity in z1 while z2 is fixed), but there is no correlation between E1 and E1
Now, we repeat the same steps as in the first part of the analysis, but with temperature and salinity having the same effect on species’ growth rate.
(#fig:plotcomm1_neg1)Community 1, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
(#fig:plotcomm2_neg1)Community 2, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
(#fig:plotcomm3_neg1) Community 3, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
Here and elsewhere in this document, the position of the optima has been estimated as the environmental location (E1 and E2 values) for which the rate is maximum.
Increasing variance in z1 - positive correlation between env variables (E1 and E2)
Same steps as before (3 communities with increasing diversity ib z1 while z2 is fixed), but the correlation between E1 and E1 is positive
Increasing variance in z1 - no correlation between env variables (E1 and E2)
Same steps as before (3 communities with increasing diversity in z1 while z2 is fixed), but there is no correlation between E1 and E1
Now we do the same, but having also z2 changing together with z1 with positive correlation. So, diversity in z1 and z2 are increasing gradually from low to high in the 3 communities.
Increasing variance in z1 and z2 - negative correlation between environmental variables (E1 and E2)
We now create 3 communities. Community 1 is characterized by low diversity in z1 and z2, community 2 has medium diversity in z1 and z2, and community 3 has high diversity in z1 and z2.
E1 and E2 have high fluctuations and negative correlation.
(#fig:plotcomm1_pos.1)Community 1, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
(#fig:plotcomm2_pos.1)Community 2, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
(#fig:plotcomm3_pos.1) Community 3, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
Here and elsewhere in this document, the position of the optima has been estimated as the environmental location (E1 and E2 values) for which the rate is maximum.
Increasing variance in z1 and z2 - positive correlation between env variables (E1 and E2)
Same steps as before (3 communities with increasing diversity in z1 while z2 is fixed), but the correlation between E1 and E1 is positive
Increasing variance in z1 - no correlation between env variables (E1 and E2)
Same steps as before (3 communities with increasing diversity in z1 while z2 is fixed), but there is no correlation between E1 and E1
Now we do the same, but having also z2 changing together with z1 with negative correlation. So, diversity in z1 is increasing gradually from low to high in the 3 communities, while z2 decreases gradually in the 3 communities.
Increasing variance in z1 and z2 - negative correlation between env variables (E1 and E2)
We now create 3 communities. Community 1 is characterized by low diversity in z1 and high diversity in z2, community 2 has medium diversity in z1 and z2, and community 3 has high diversity in z1 and low in z2.
E1 and E2 have high fluctuations and negative correlation.
(#fig:plotcomm1_mix.1.2)Community 1, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
(#fig:plotcomm2_mix.1.2)Community 2, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
(#fig:plotcomm3_mix.1.2) Community 3, single species responses. (a) Species responses to the gradient of E1. Different colour lines show the dependency of the rate to the second environmental variable (E2). (b) Species responses to the gradient of E2. Different colour lines show the dependency of the rate to the second environmental variable (E1).
Here and elsewhere in this document, the position of the optima has been estimated as the environmental location (E1 and E2 values) for which the rate is maximum.
Increasing variance in z1 and z2 - positive correlation between env variables (E1 and E2)
Same steps as before (3 communities with increasing diversity ib z1 while z2 is fixed), but the correlation between E1 and E1 is positive
Increasing variance in z1 - no correlation between env variables (E1 and E2)
Same steps as before (3 communities with increasing diversity in z1 while z2 is fixed), but there is no correlation between E1 and E1
Figure 7.1: Potential response diversity
Figure 7.2: Summary plot showing the effects of the determinants on directional response diveristy measured as Dissimilarity
(#fig:SummaryPlot1.4)Summary plot showing the effects of the determinants on directional response diveristy measured as Divergence (same as in the main manuscript